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Stochastic non-linear oscillators

Part of: Equations and systems with randomness Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Lawrence Markus  and
Ananda Weerasinghe
Lawrence Markus*
Affiliation:
University of Minnesota
Ananda Weerasinghe*
Affiliation:
Iowa State University
*
∗ Postal address: Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
∗∗ Postal address: Department of Mathematics, Iowa State University, Ames, IA 50011, USA.
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Abstract

Non-linear stochastic systems driven by white noise are analysed from the viewpoint of non-linear oscillation theory. Under various familiar hypotheses concerning dissipative and restorative dynamical forces, the existence and uniqueness, asymptotic growth, and oscillatory behavior of the solutions are demonstrated.

Keywords

STOCHASTIC DIFFERENTIAL EQUATIONSOSCILLATIONS

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60H20: Stochastic integral equations 34F05: Equations and systems with randomness
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 3 , September 1993 , pp. 649 - 666
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research partially supported by NSF grants DMS 88–02792 and DMS 88–03639.

References

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